Vulnerability to paroxysmal oscillations in delayed neural networks: A basis for nocturnal frontal lobe epilepsy?

Chaos

Volumn 21, Issue 4, 2011, Pages

  Quan, Austin ^a,d   Osorio, Ivan ^b   Ohira, Toru ^c,e   Milton, John ^c  

^a HARVEY MUDD COLLEGE   (United States)

^b UNIVERSITY OF KANSAS SCHOOL OF MEDICINE   (United States)

^c KECK GRADUATE INSTITUTE   (United States)

^d Interthinx   (United States)

^e SONY COMPUTER SCIENCE LABORATORIES INC   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ARTICLE; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; COMPUTER SIMULATION; FRONTAL LOBE; FRONTAL LOBE EPILEPSY; HUMAN; NERVE CELL; NERVE CELL NETWORK; PATHOPHYSIOLOGY; SLEEP STAGE;

ACTION POTENTIALS; BIOLOGICAL CLOCKS; COMPUTER SIMULATION; EPILEPSY, FRONTAL LOBE; FRONTAL LOBE; HUMANS; MODELS, NEUROLOGICAL; NERVE NET; NEURONS; SLEEP STAGES;

EID: 84855272276     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3664409     Document Type: Article

References (56)

1. Goldberger A.L. Ann. Biomed. Eng. 1990, 18:195. 10.1007/BF02368429.
2. Zbilut J.P. Unstable Singularities and Randomness: Their Importance in the Complexity of Physical, Biochemical and Social Systems 2004, (Elsevier, New York).
3. Muezzinoglu M.K. Tristan I. Huerta R. Afraimovich V.S. Rabinovich M.I. Int. J. Bifurcation Chaos 2010, 20:1653. 10.1142/S0218127410026745
4. Milton J.G. Cabrera J.L. Ohira T. EPL 2008, 83:48001. 10.1209/0295-5075/83/48001
5. Eurich C.W. Milton J.G. Phys. Rev. E 1996, 54:6681. 10.1103/PhysRevE.54.6681
6. Foss J. Moss F. Milton J. Phys. Rev. E 1997, 55:4536. 10.1103/PhysRevE.55.4536
7. Grotta-Ragazzo C. Pakdaman K. Malta C.P. Phys. Rev. E 1999, 60:6230. 10.1103/PhysRevE.60.6230
8. Pakdaman K. Grotta-Ragazzo C. Malta C.P. Phys. Rev. E 1998, 58:3623. 10.1103/PhysRevE.58.3623
9. Pakdaman K. Grotta-Ragazzo C. Malta C.P. Arino O. Vibert J.-F. Neural Networks 1998, 11:509. 10.1016/S0893-6080(97)00112-3
10. Ohira T. Sato Y. Phys. Rev. Lett. 1999, 82:8111. 10.1103/PhysRevLett.82.2811
11. Tsimring L. Pikovsky A. Phys. Rev. Lett. 2001, 87:250602. 10.1103/PhysRevLett.87.250602
12. Milton J. Naik P. Chan C. Campbell S.A. Math. Model. Nat. Phenom. 2010, 5:125. 10.1051/mmnp/20105205
13. Milton J.G. Quan A.R. Osorio I. Epilepsy: Intersection of Neurosciences, Biology, Mathematics, Engineering and Physics 2011, 501-510. I. Osorio, H. P. Zaveri, M. G. Frei, S. Arthurs, and in edited by and (CRC Press, Boca Raton, New York)
14. Hofstra W.A. Gordijn M.C. van der Palen J. van Regteren R. Grootemarsink B.E. de Weerd A.W. Epilepsy Res. 2011, 94:158. 10.1016/j.eplepsyres.2011.01.015
15. Elliott W.J. Stroke 1998, 29:992. 10.1161/01.STR.29.5.992.
16. Manfredini R. Gallerani M. Salmi R. Caló G. Pasin M. Bigoni M. Fersini C. J. Emergency Med. 1994, 12:5. 10.1016/0736-4679(94)90003-5
17. Viskin S. Golovner M. Malov N. Fish R. Alroy I. Vila Y. Laniado S. Kaplinsky E. Roth A. Eur. Heart J. 1999, 20:1429. 10.1053/euhj.1999.1632
18. Savopoulos C. Ziakas A. Hatzitolios A. Delivoria C. Kounanis A. Mylonas S. Tsourgas M. Psaroulis D. Angiology 2006, 57:197. 10.1177/000331970605700210
19. Steinlein O.K. Bertrand D. Pflugers Arch. 2009, 460:495. 10.1007/s00424-009-0766-8
20. Motamedi G.K. Lesser R.P. Epilepsy: Intersection of Neurosciences, Biology, Mathematics, Engineering and Physics 2011, 445-450. I. Osorio, H. P. Zaveri, M. G. Frei, S. Arthurs, and in edited by and (CRC Press, Boca Raton, New York)
21. Mackey M.C. Glass L. Science 1977, 197:287. 10.1126/science.267326
22. Glass L. Mackey M.C. Ann. N.Y. Acad. Sci. 1979, 316:214. 10.1111/j.1749-6632.1979.tb29471.x
23. Glass L. Mackey M.C. From Clocks to Chaos: The Rhythms of Life 1988, and (Princeton University Press, Princeton, NJ).
24. Milton J.G. Epilepsy Behav. 2010, 18:33. 10.1016/j.yebeh.2010.03.002.
25. Milton J.G. Gotman J. Remillard G.M. Andermann F. Epilepsia 1987, 28:471. 10.1111/j.1528-1157.1987.tb03675.x
26. Epilepsy as a dynamic disease 2003, J. Milton, P. Jung, edited by and (Springer, New York).
27. Lopes da Silva F.H. Blanes W. Kalitzin S.N. Parra J. Suffczynski P. Velis D.N. IEEE Trans. Biomed. Eng. 2003, 50:540. 10.1109/TBME.2003.810703
28. Milton J.G. Self-organized Biological Dynamics & Nonlinear Control 2000, 374-386. J. Walleczek, in edited by (Cambridge University Press: New York)
29. Tuller B. Case P. Ding M. Kelso J.A. S. J. Exp. Psychol. Human Percept. Perform. 1994, 20:2. 10.1037/0096-1523.20.1.3
30. Kelso J.A. S. Dynamic Patterns: The Self-Organization of Brain and Behavior 1999, (MIT Press, Cambridge, MA).
31. Osorio I. Frei M.G. Int. J. Neural Syst. 2009, 19:1. 10.1142/S0129065709001926
32. Lesser R.P. Kim S.H. Beyderman L. Miglioretti D.L. Webber W.R. Bare M. Cysyk B. Krauss G. Gordon B. Neurology 1999, 53:2073. and [PMID: 10599784].
33. Motamedi G.K. Lesser R.P. Miglioretti D.L. Mizuono-Matsumoto Y. Gordon B. Webber W.R. S. Jackson D.C. Sepkaty J.P. Crone N.E. Epilepsia 2002, 43:836. 10.1046/j.1528-1157.2002.24901.x
34. Herzog A.G. Seizure 2008, 17:151. 10.1016/j.seizure.2007.11.014.
35. Temkin N.R. Davis J.R. Epilepsia 1984, 25:450. 10.1111/j.1528-1157.1984.tb03442.x
36. Wiesenfeld K. Moss F. Nature 1995, 373:33. 10.1038/373033a0
37. Gammaitoni L. Marchesoni F. Menichella-Saetta E. Santucci S. Phys. Rev. Lett. 1989, 62:349. 10.1103/PhysRevLett.62.349
38. Parzen E. Stochastic Processes 1999, (SIAM Classics in Applied Mathematics, Philadelphia).
39. Shumway R.H. Stiffer D.S. Time Series Analysis and Its Applications with R examples 2011, and 3rd ed. (Springer, New York).
40. Gammaitoni L. Hänngi P. Jung P. Marchesoni F. Rev. Mod. Phys. 1998, 70:1223. 10.1103/RevModPhys.70.223
41. Rabinovich M.I. Varona P. Selveston A.I. Abarbanel H.D. I. Rev. Mod. Phys. 2006, 78:1213. 10.1103/RevModPhys.78.1213
42. Rabinovich M. Huerta R. Laurent G. Science 2008, 321:48. 10.1126/science.1155564
43. Osorio I. Frei M.G. Sornette D. Milton J. Lai Y.-C. Phys. Rev. E 2010, 82:021919. 10.1103/PhysRevE.82.021919
44. Stead M. Bower M. Brinkman B.H. Lee K. Marsh W.R. Meyer F.B. Litt B. Van Gompel J. Worrell G.A. Brain 2010, 133:2789. 10.1093/brain/awq190
45. Goodfellow M. Schindler K. Baier G. NeuroImage 2011, 55:920. 10.1016/j.neuroimage.2010.12.074
46. Visser S. Meijer H.G. E. Lee H.C. van Dromgelen W. Putten M.J. A. M. van Gils S.A. J. Clin. Neurophysiol. 2010, 27:471. 10.1097/WNP.0b013e3181fe0735
47. Day J. Rubin J.E. Chow C.C. SIAM J. Appl. Dyn. Syst. 2009, 8:1523. 10.1137/080718929
48. Hastings A. Trends Ecol. Evol. 2004, 19:39. 10.1016/j.tree.2003.09.007.
49. Caswell H. Neubert M.G. J. Differ. Equ. Appl. 2005, 11:295. 10.1080/10236190412331335382
50. Babloyantz A. Destrexhe A. Proc. Natl. Acad. Sci. USA 1986, 83:3513. 10.1073/pnas.83.10.3513
51. Schaffer W.M. Kendall B.E. Tidd C.W. IMA J. Math. Appl. Med. Biol. 1993, 10:227. 10.1093/imammb/10.4.227
52. Pierson D. Moss F. Phys. Rev. Lett. 1995, 75:2124. 10.1103/PhysRevLett.75.2124
53. Insperger T. IEEE Trans. Controlled Syst. Technol. 2006, 14:974. 10.1109/TCST.2006.876938.
54. Stépán G. Insperger T. Ann. Rev. Control 2006, 30:159. 10.1016/j.arcontrol.2006.08.002
55. Grebogi C. Ott E. Yorke J.A. Phys. Rev. Lett. 1986, 57:1284. 10.1103/PhysRevLett.57.1284
56. Baer S.M. Gaekel E.M. Phys. Rev. E 2008, 78:036205. 10.1103/PhysRevE.78.036205